Question: Simplify the following expression: $a = \dfrac{-10q^2 - 30q + 40}{q - 1} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-10$ , so we can rewrite the expression: $ a =\dfrac{-10(q^2 + 3q - 4)}{q - 1} $ Then we factor the remaining polynomial: $q^2 + {3}q {-4} $ ${-1} + {4} = {3}$ ${-1} \times {4} = {-4}$ $ (q {-1}) (q + {4}) $ This gives us a factored expression: $\dfrac{-10(q {-1}) (q + {4})}{q - 1}$ We can divide the numerator and denominator by $(q + 1)$ on condition that $q \neq 1$ Therefore $a = -10(q + 4); q \neq 1$